We present an O(n(3))-time, O(n(2))-space algorithm to test whether a dissimilarity d on an n-object set X is Robinsonian, i.e., X admits an ordering such that i less than or equal to j less than or equal to k implies...
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We present an O(n(3))-time, O(n(2))-space algorithm to test whether a dissimilarity d on an n-object set X is Robinsonian, i.e., X admits an ordering such that i less than or equal to j less than or equal to k implies that d(x(i),x(k)) greater than or equal to max {d(x(i),x(j)), d(x(j),x(k))}.
We use the technique of divide-and-conquer to construct a rectilinear Steiner minimal tree on a set of sites in the plane. A well-known optimal algorithm for this problem by Dreyfus and Wagner [10] is used to solve th...
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We use the technique of divide-and-conquer to construct a rectilinear Steiner minimal tree on a set of sites in the plane. A well-known optimal algorithm for this problem by Dreyfus and Wagner [10] is used to solve the problem in the base case. The run time of our optimal algorithm is probabilistic in nature: for all epsilon > 0, there exists b > 0 such that Prob[T(n) < 2b square-root n log n] > 1 - epsilon, for n sites uniformly distributed on a rectangle. The key fact in the run-time argument is the existence of probable bounds on the number of edges of an optimal tree crossing our subdivision lines. We can test these bounds in low-degree polynomial time for any given set of sites. (C) 1994 John Wiley & Sons, Inc.
AnO(n logn) divide-and-conquer algorithm for finding the relative neighborhood graph RNG(V) of a set V ofn points in Euclidean space is presented. If implemented in parallel, its time complexity isO(n) and it requires...
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AnO(n logn) divide-and-conquer algorithm for finding the relative neighborhood graph RNG(V) of a set V ofn points in Euclidean space is presented. If implemented in parallel, its time complexity isO(n) and it requiresO(logn) processors.
The goal of this paper is to describe a rather general approach for constructing upper and lower bounds for the average computational complexity of divide-and-conquer algorithms.
The goal of this paper is to describe a rather general approach for constructing upper and lower bounds for the average computational complexity of divide-and-conquer algorithms.
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